Linear Time Series


The first part of this course is devoted to studying univariate time series: first we present the principal statistical concepts, then estimation methods and tests; we examine the non-stationarity problem by studying the main unit root tests from a practical angle. The course is illustrated with practical examples. The second part of the course is devoted to studying stationary VAR models: we briefly present the general framework of multivariate stationary series before developing the specific case of VAR models. Finally, we take a quick look at the principles of cointegration.



  1. General remarks on second-order univariate stationary processes– Auto-covariances, partial and inverse auto-correlations, spectral density, innovation process. Statement of Wold’s theorem. Statement of the asymptotic properties of empirical moments.
  2. AR, MA, ARMA, ARIMA processes– Definitions, canonical representation, properties, concept of initial condition, unit root tests. Identification, estimation and tests, forecasting.
  3. Stationary vector processes –Formal framework for studying these models, canonical representation and Wold representation, innovation process, stationary VAR models. Estimation, forecasting, causality tests, impulse-response function.
  4. Non-stationary vector processes and definition of cointegration –Cointegrated non-stationary VAR models and error-correction models. Estimation in a cointegrated VAR model. Cointegration tests: practical use.



Brockwell P.J., R.A. Davis : Time Series : Theory and Methods, Springer Verlag [24 BRO 00 A]Gouriéroux C., A. Monfort Séries Temporelles et Modèles Dynamiques, Economica [24 GOU 00 B]Hamilton J.D. Time Series Analysis, Princeton Univ. Press [24 HAM 00 A]Lutkepohl H. Introduction to Multiple Time Series Analysis, Springer Verlag. [24 LUT 00 B]Johansen S. Likelihood Based Inference in Cointegrated Vector Auto-Regression Models, Oxford University Press. [28 JOH 02 A]